Barely. Not enough to be a hinderance to mutual understanding.

To me, the proper pronunciation of Jacques sounds more like "Jock", so it does seem to be more than barely significant.

Does this https://www.bing.com/videos/riverview/relatedvideo?q=Jacques... really sound like Jock to you? There is a significant sharp "æ" sound, the same as in Jack/dʒæk

It sounds like [a] to me, not [æ].

The a in the name Jacques is pronounced as in the word father.

The a in the name Jack is pronounced as in cat.

As someone who has heard the name "Jack" pronounced by Americans many, many, many times in their life... that Jaques video sounds entirely in-range of the variety of pronunciations I hear for Jack.

Well, as one particular American, who has spoken to many, many other Americans in their life, I can only tell you what I think.

Something I find interesting is that Americans say the a in the word taco (a word borrowed from Spanish) with the a as in father, that is, [ɑː], but English people say the a as in cat, [æ]. Different dialects approximate the Spanish [a] differently.